Wilkinson lauded Beckford's goal-scoring attributes as Newcastle United attempted to prise the League One leaders' 20-goal leading scorer away from Elland Road for a cut-price £1.5 million.
But Wilkinson has admitted Leeds United may be unable to retain the services of their prize asset whose submission of a transfer request came to light following his winner in the 1-0 FA Cup victory over arch-rivals Manchester United.
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"It is the ultimate act. It is the moment of truth. It is such a priceless asset to have. If you have got it then you are very fortunate."
Wilkinson, who steered Leeds to the League Championship in 1992, added: "I am sure that (current Leeds manager) Simon Grayson is desperately hoping that he can hang on to him and push on to promotion which at this moment in time looks inevitable.
"I don't have any thoughts on whether he should go or stay. You never know what is going on behind the scenes but he was certainly a problem whenever he was on the shoulder of the Man United centre backs. "
"The big thing about that is that as a football club then you can own a player's body. That is in his contract. But whether you own his head or his heart that is sometimes out of your hands.
"I would have thought that goal would have strengthened his affinity with the club and the fans but in football these days the business aspect of it is bigger."
Wilkinson saw his former club record a famous victory at Old Trafford and even though Beckford may not remain with the Yorkshire he is convinced Grayson's team will go from strength to strength.
"As far as Simon is concerned it was one of those games where they came out of the game a better team than the one that went into it and that is always a great benefit," Wilkinson added.
"Leeds gave a good account of themselves against the Premier League champions and at no point looked overawed by the situation which is what can happen to teams at Old Trafford. Teams got out and play the stadium and not the opposition on the field of play.
"It is a different team and a different era to when I was there at Leeds and Simon is his own man and he has his own way of doing things. The only thing that has stayed the same is the undoubted enthusiasm of the supporters. When you see the better bits of Leeds United supporters you won't see any better."